She added that she had received a “large volume of calls in relation this matter” from people seeking assurances “about a number of aspects of the policy”.

Under the Education Act 1996, pupils must learn about the nature of marriage and its importance for family life and the bringing up of children.

Her letter, leaked to the Daily Mail, was sent after Mrs Miller detailed her plans to MPs. The letter was copied to Michael Gove, the Education Secretary, Chris Grayling, the Justice Secretary, Eric Pickles, the Communities Secretary, and Dominic Grieve, the Attorney General.

The Cabinet signed off the gay marriage plans this week, but Lady Warsi’s letter suggests that serious reservations remain.

Her intervention came as the Church of England said it could one day conduct same-sex weddings despite its vocal opposition to the idea.

The Church signalled acceptance of the Government’s plans to allow gay couples to marry as long as churches are not forced to perform the ceremonies.

Officials have acknowledged that the established Church could potentially “live with” the proposals drawn up by government lawyers to prevent churches facing human rights challenges to force them to conduct weddings for homosexual couples.

The admission was made despite claims earlier this year that same-sex marriage could pose the biggest threat to its position as the established church since the Reformation.

The Archbishop of Canterbury designate, the Rt Rev Justin Welby, has also made clear that he is opposed to same-sex marriage.

Yesterday, the House of Lords heard that several bishops secretly support the principle of gay marriage itself but are afraid to speak out because it would contradict the official policy of the Church.

Mrs Miller outlined a “quadruple lock” system of legal protections for churches on Tuesday.

She told the Commons that any legislation would explicitly state that it would be “illegal” for the Church of England to conduct same-sex weddings even if they became law in the country.

In its first official response to the announcement, the Church issued a statement dismissing the idea that this meant it would be “banned” from carrying out same-sex weddings if it chose to.

Such an assumption was “based on a misunderstanding” of the Church of England’s legal status.

“This is not a question of the Government and Parliament imposing a prohibition or 'ban’ on what the Church of England can do,” it said in a statement drafted on advice from canon lawyers.

“The effect of what the Government has proposed is to leave decisions about the doctrine and practice of the Church of England with the Church of England.”

It went on to explain that the Church would be free to carry out same-sex weddings if the General Synod approved a change to Church law.